Transmit methods with delay diversity and space-frequency diversity

ABSTRACT

In this invention, several open-loop solutions that encompass the small delay CDD codeword cycling, codeword cycling between different re-transmissions of both small and large delay CDD are proposed. In addition, an open-loop codeword cycling method for SFBC+FSTD scheme, as well as its extension to SFBC+FSTD based HARQ, are proposed. In one method, a plurality of information bits are encoded, scrambled and modulated to generate a plurality of modulation symbols. The plurality of modulation symbols are mapped onto the subcarriers in at least one transmission layer of a transmission resource. The modulation symbols are then precoded by using a matrix for cyclic delay diversity and a set of codewords from a certain codebook to generate a plurality of precoded symbols. The codewords are cycled for every a certain number of subcarriers. Finally, the precoded symbols are transmitted via a plurality of transmission antennas.

CLAIM OF PRIORITY

This application makes reference to, incorporates the same herein, andclaims all benefits accruing under 35 U.S.C. § 119 from a provisionalapplication earlier filed in the U.S. Patent & Trademark Office on 25Jun. 2007 and there duly assigned Ser. No. 60/929,376.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to methods to transmit signal by usingdelay diversity and space frequency diversity.

2. Description of the Related Art

This application, pursuant to 37 C.F.R. §1.57, incorporates by referencethe following publications, copies of same material are annexed to thisspecification, and which are made a part of this application:

[1]. 3GPP RAN1 contribution R1-072461, “High Delay CDD in Rank AdaptedSpatial Multiplexing Mode for LTE DL”, May 2007, Kobe, Japan;

[2]. 3GPP RAN1 contribution R1-072019, “CDD precoding for 4 Txantennas”, May 2007, Kobe, Japan;

[3]. 3GPP TS 36.211, “Physical Channels and Modulation”, v 1.1.0;

[4]. U.S. Provisional Patent Application Ser. No. 60/929,027 filed on6^(th) of June, 2007, “CDD Precoding for open-loop SU MIMO”;

[5]. 3GPP RAN1 contribution R1-073096, “Text Proposal for 36.211regarding CDD Design”, June 2007, Orlando, USA; and

[6]. 3GPP TS 36.211, “Physical Channels and Modulation”, v 8.2.0.

A typical cellular radio system includes a number of fixed base stationsand a number of mobile stations. Each base station covers a geographicalarea, which is defined as a cell.

Typically, a non-line-of-sight (NLOS) radio propagation path existsbetween a base station and a mobile station due to natural and man-madeobjects disposed between the base station and the mobile station. As aconsequence, radio waves propagate while experiencing reflections,diffractions and scattering. The radio wave which arrives at the antennaof the mobile station in a downlink direction, or at the antenna of thebase station in an uplink direction, experiences constructive anddestructive additions because of different phases of individual wavesgenerated due to the reflections, diffractions, scattering andout-of-phase recombination. This is due to the fact that, at highcarrier frequencies typically used in a contemporary cellular wirelesscommunication, small changes in differential propagation delaysintroduces large changes in the phases of the individual waves. If themobile station is moving or there are changes in the scatteringenvironment, then the spatial variations in the amplitude and phase ofthe composite received signal will manifest themselves as the timevariations known as Rayleigh fading or fast fading attributable tomultipath reception. The time-varying nature of the wireless channelrequire very high signal-to-noise ratio (SNR) in order to providedesired bit error or packet error reliability.

The scheme of diversity is widely used to combat the effect of fastfading by providing a receiver with multiple faded replicas of the sameinformation-bearing signal.

The schemes of diversity in general fall into the following categories:space, angle, polarization, field, frequency, time and multipathdiversity. Space diversity can be achieved by using multiple transmit orreceive antennas. The spatial separation between the multiple antennasis chosen so that the diversity branches, i.e., the signals transmittedfrom the multiple antennas, experience fading with little or nocorrelation. Transmit diversity, which is one type of space diversity,uses multiple transmission antennas to provide the receiver withmultiple uncorrelated replicas of the same signal. Transmissiondiversity schemes can further be divided into open loop transmitdiversity and closed-loop transmission diversity schemes. In the openloop transmit diversity approach no feedback is required from thereceiver. In one type of closed loop transmit diversity, a receiverknows an arrangement of transmission antennas, computes a phase andamplitude adjustment that should be applied at the transmitter antennasin order to maximize a power of the signal received at the receiver. Inanother arrangement of closed loop transmit diversity referred to asselection transmit diversity (STD), the receiver provides feedbackinformation to the transmitter regarding which antenna(s) to be used fortransmission.

Cyclic Delay Diversity (CDD) is a diversity scheme used in OFDM-basedtelecommunication systems, transforming spatial diversity into frequencydiversity avoiding inter symbol interference.

The 3rd Generation Partnership Project (3GPP) contribution R1-072633, TS36.211 version 1.1.0, proposed a CDD precoder structure that requires aPrecoder Matrix Indication (PMI) feedback. Also, in the CDD described inTS 36.211 version 1.1.0, the open loop (i.e., large delay) and closedloop (i.e., small delay CDD) structures are different. It would bebetter to have one structure for both open loop and closed loop, byusing different values of the precoder. The two structures are identicalfor the full rank cases and where the precoder matrix is an identitymatrix. The closed loop structure has no solution for the case where noPMI is available for the less than full rank case. In the U.S.provisional application 60/929,027 filed on 8 Jun. 2007, entitled “CDDprecoding for open-loop SU MIMO”, an open-loop solution is proposed forimproving the large delay CDD scheme in the high speed scenarios.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide improvedmethods and apparatus for transmitting signals.

It is another object of the present invention to provide an improvedopen loop precoder that can be applied to both large delay CDD and smalldelay CDD diversity schemes during transmission.

According to one aspect of the present invention, a plurality ofinformation bits are encoded, scrambled and modulated to generate aplurality of modulation symbols. The plurality of modulation symbols aremapped onto the subcarriers in at least one transmission layer of atransmission resource. The modulation symbols are then precoded by usinga matrix for cyclic delay diversity and a set of codewords from acertain codebook to generate a plurality of precoded symbols. Thecodewords are cycled for every a certain number of subcarriers. Finally,the precoded symbols are transmitted via a plurality of transmissionantennas.

For large delay CDD, the precoded symbols corresponding to the i-thsubcarrier is:

y(i)=W(i)·D(i)·U·x(i),

where x(i) is a block of modulation symbols corresponding to the i-thsubcarrier and x(i)=[x⁽⁰⁾(i) . . . x^((ν-1))(i)]^(T), ν is the number oftransmission layers, U is a certain fixed matrix and the elements of Ubeing established by U_(mn)=e^(−j2πmn/ν) for m=0, 1, . . . , ν−1, andn=0, 1, . . . , ν−1, and D(i) is a diagonal matrix for supporting largedelay cyclic delay diversity.

For small delay CDD, the precoded symbols corresponding to the i-thsubcarrier is:

y(i)=D(i)·W(i)·x(i),

where D(i) is a diagonal matrix for supporting small delay cyclic delaydiversity.

For both small delay CDD and large delay CDD, the precoded symbolscorresponding to the i-th subcarrier is:

y(i)=D(i)·W(i)·C(i)·x(i),

where D(i) is a first diagonal matrix for supporting small delay cyclicdelay diversity, and C(i) is a second diagonal matrix for supportinglarge delay cyclic delay diversity.

The value q may be equal to 1, or may be equal to the transmission rank,or may be equal to 12 m, where m is a positive integer.

The set of code words may include all of the codewords in the certaincodebook. Alternatively, the set of code words may include a subset ofcodewords in the certain codebook.

According to another aspect of the present invention, a plurality ofinformation bits are encoded, scrambled and modulated to generate aplurality of modulation symbols. The plurality of modulation symbols aremapped onto the subcarriers in at least one transmission layer of atransmission resource. The mapped symbols are repeatedly precoded andtransmitted via a plurality of antennas by using a matrix for cyclicdelay diversity and applying different codewords for differentretransmissions.

According to yet another aspect of the present invention, four symbolsto be transmitted are encoded by using a rank-2 space frequency blockcode to generate a rank-2 space frequency block of symbols. Then, theblock of symbols are precoded by using a matrix for cyclic delaydiversity and a set of codewords from a certain codebook to generate aplurality of precoded symbols. The codewords cycled for every a certainnumber of subcarriers. Finally, the precoded symbols are transmitted viaa plurality of antennas.

According to still yet another aspect of the present invention, foursymbols to be transmitted are encoded by using a rank-2 space frequencyblock code to generate a rank-2 space frequency block of symbols. Theblock of symbols are repeatedly precoded and transmitted via a pluralityof antennas by using a matrix for cyclic delay diversity and applyingdifferent codewords for different retransmissions.

According to a further aspect of the present invention, four symbols tobe transmitted are encoded to generate two transmission matrices. Thetwo transmission matrices T₁ and T₂ are:

$\begin{matrix}{T_{1} = \begin{bmatrix}T_{11} & T_{12} & T_{13} & T_{14} \\T_{21} & T_{22} & T_{23} & T_{24} \\T_{31} & T_{32} & T_{33} & T_{34} \\T_{41} & T_{42} & T_{43} & T_{44}\end{bmatrix}} \\{{= \begin{bmatrix}S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0 \\0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*}\end{bmatrix}},}\end{matrix}$ and $\begin{matrix}{T_{2} = \begin{bmatrix}T_{11} & T_{12} & T_{13} & T_{14} \\T_{21} & T_{22} & T_{23} & T_{24} \\T_{31} & T_{32} & T_{33} & T_{34} \\T_{41} & T_{42} & T_{43} & T_{44}\end{bmatrix}} \\{{= \begin{bmatrix}0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*} \\S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0\end{bmatrix}},}\end{matrix}$

where T_(ij) represents the symbol to be transmitted on the ith antennaand the jth subcarrier. The four symbols are repeatedly transmitted viafour antennas by alternatively applying the two transmission matrices T₁and T₂ in a frequency domain.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the invention and many of the attendantadvantages thereof, will be readily apparent as the same becomes betterunderstood by reference to the following detailed description whenconsidered in conjunction with the accompanying drawings in which likereference symbols indicate the same or similar components, wherein:

FIG. 1 schematically illustrates an Orthogonal Frequency DivisionMultiplexing (OFDM) transceiver chain suitable for the practice of theprinciples of the present invention;

FIGS. 2A and 2B schematically illustrate two schemes of subcarrierallocation of frequency-selective multi-user scheduling and frequencydiversity in an OFDM system;

FIG. 3 schematically illustrates a transmission and reception scheme ina multiple input and multiple output (MIMO) system;

FIG. 4 schematically illustrates a precoding scheme is a MIMO system;

FIG. 5 schematically illustrates a scheme for processing precodedsignals at a receiver;

FIGS. 6A and 6B illustrate two schemes of applying phase shift tosubcarriers;

FIG. 7 schematically illustrates a cyclic delay diversity precodingscheme;

FIG. 8 schematically illustrates using different codewords in differentretransmissions in a Hybrid automatic repeat and request (HARQ) schemeas one embodiment according to the principles of the present invention;

FIG. 9 schematically illustrates a scheme for precoding a rank-2 spacefrequency block code as another embodiment according to the principlesof the present invention;

FIG. 10 schematically illustrates a scheme for preceding a rank-2 spacefrequency block code by applying different codewords in differentretransmissions in a HARQ scheme as another embodiment according to theprinciples of the present invention; and

FIG. 11 schematically illustrates mapping of symbols to antennas for aSpace Frequency Block Code (SFBC) combined with frequency SwitchedTransmit Diversity (FSTD) scheme as still another embodiment accordingto the principles of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 illustrates an Orthogonal Frequency Division Multiplexing (OFDM)transceiver chain. In a communication system using OFDM technology, attransmitter chain 110, control signals or data 111 is modulated bymodulator 112 into a series of modulation symbols, that are subsequentlyserial-to-parallel converted by Serial/Parallel (S/P) converter 113.Inverse Fast Fourier Transform (IFFT) unit 114 is used to transfer thesignals from frequency domain to time domain into a plurality of OFDMsymbols. Cyclic prefix (CP) or zero prefix (ZP) is added to each OFDMsymbol by CP insertion unit 116 to avoid or mitigate the impact due tomultipath fading. Consequently, the signal is transmitted by transmitter(Tx) front end processing unit 117, such as an antenna (not shown), oralternatively, by fixed wire or cable. At receiver chain 120, assumingperfect time and frequency synchronization are achieved, the signalreceived by receiver (Rx) front end processing unit 121 is processed byCP removal unit 122. Fast Fourier Transform (FFT) unit 124 transfers thereceived signal from time domain to frequency domain for furtherprocessing.

The total bandwidth in an OFDM system is divided into narrowbandfrequency units called subcarriers. The number of subcarriers is equalto the FFT/IFFT size N used in the OFDM system. In general, the numberof subcarriers used for data is less than N because some subcarriers atthe edge of the frequency spectrum are reserved as guard subcarriers. Ingeneral, no information is transmitted on guard subcarriers.

In a communication link, a multi-path channel results in afrequency-selective fading. Moreover, in a mobile wireless environment,the channel also results in a time-varying fading. Therefore, in awireless mobile system employing OFDM based access, the overall systemperformance and efficiency can be improved by using, in addition totime-domain scheduling, frequency-selective multi-user scheduling. In atime-varying frequency-selective mobile wireless channel, it is alsopossible to improve the reliability of the channel by spreading and/orcoding the information over the subcarriers.

In case of frequency-selective multi-user scheduling, a contiguous setof subcarriers potentially experiencing an upfade is allocated fortransmission to a user. The total bandwidth is divided into subbandsgrouping multiple contiguous subcarriers as shown in FIG. 2A wheresubcarriers f₁, f₂, f₃ and f₄ are grouped into a subband fortransmission to a user in frequency-selective multi-user schedulingmode. In case of frequency-diversity transmission, however, theallocated subcarriers are preferably uniformly distributed over thewhole spectrum. As shown in FIG. 2B, subcarriers f₁, f₅, f₉ and f₁₃ aregrouped into a subband for transmission. The frequency-selectivemulti-user scheduling is generally beneficial for low mobility users forwhich the channel quality can be tracked. But the channel qualitygenerally can not be tracked for high mobility users (particularly in afrequency-division-duplex system where the fading between the downlinkand uplink is independent) due to channel quality feedback delays andhence the frequency diversity transmission mode is preferred.

Multiple Input Multiple Output (MIMO) schemes use multiple transmitantennas and multiple receive antennas to improve the capacity andreliability of a wireless communication channel. A MIMO system promiseslinear increase in capacity with K where K is the minimum of number oftransmit (M) and receive antennas (N), i.e. K=min (M,N). A simplifiedexample of a 4×4 MIMO system is shown in FIG. 3. In this example, fourdifferent data streams are transmitted separately from the four transmitantennas. The transmitted signals are received at the four receiveantennas. Some form of spatial signal processing is performed on thereceived signals in order to recover the four data streams. An exampleof spatial signal processing is vertical Bell Laboratories LayeredSpace-Time (V-BLAST) which uses the successive interference cancellationprinciple to recover the transmitted data streams. Other variants ofMIMO schemes include schemes that perform some kind of space-time codingacross the transmit antennas (e.g., diagonal Bell Laboratories LayeredSpace-Time (D-BLAST)) and also beamforming schemes such as SpatialDivision multiple Access (SDMA).

The MIMO channel estimation consists of estimating the channel gain andphase information for links from each of the transmit antennas to eachof the receive antennas. Therefore, the channel for M×N MIMO systemconsists of an N×M matrix:

$\begin{matrix}{H = \begin{bmatrix}a_{11} & a_{12} & \ldots & a_{1M} \\a_{21} & a_{22} & \ldots & a_{2M} \\\vdots & \vdots & \ddots & \vdots \\a_{N\; 1} & a_{N\; 2} & \ldots & a_{NM}\end{bmatrix}} & (1)\end{matrix}$

where a_(ij) represents the channel gain from transmit antenna j toreceive antenna i. In order to enable the estimations of the elements ofthe MIMO channel matrix, separate pilots are transmitted from each ofthe transmit antennas.

An optional precoding protocol that employs a unitary pre-coding beforemapping the data streams to physical antennas is shown in FIGS. 5A and5B. The optional precoding creates a set of virtual antennas (VA) 171before the pre-coding. In this case, each of the codewords ispotentially transmitted through all the physical transmission antennas172. Two examples of unitary precoding matrices, P₁ and P₂ for the caseof two transmission antennas 172 may be:

$\begin{matrix}{{P_{1} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}},{P_{2} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}}}} & (2)\end{matrix}$

Assuming modulation symbols S₁ and S₂ are transmitted at a given timethrough stream 1 and stream 2 respectively. Then the modulation symbolT₁ after preceding with matrix P₁ in the example as shown in FIG. 5A andthe modulation symbol T₂ after precoding with matrix P₂ in the exampleas shown in FIG. 5B can be respectively written as:

$\begin{matrix}{{T_{1} = {{P_{1}\begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} = {{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}} \times \begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} = {\frac{1}{\sqrt{2}}\begin{bmatrix}{S_{1} + S_{2}} \\{S_{1} - S_{2}}\end{bmatrix}}}}}{T_{2} = {{P_{2}\begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} = {{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}} \times \begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} = {\frac{1}{\sqrt{2}}\begin{bmatrix}{S_{1} + S_{2}} \\{{j\; S_{1}} - {j\; S_{2}}}\end{bmatrix}}}}}} & (3)\end{matrix}$

Therefore, the symbols

$T_{11} = {{\frac{( {S_{1} + S_{2}} )}{\sqrt{2}}\mspace{11mu} {and}\mspace{14mu} T_{12}} = \frac{( {S_{1} - S_{2}} )}{\sqrt{2}}}$

will be transmitted via antenna 1 and antenna 2, respectively, whenprecoding is done using precoding matrix P₁ as shown in FIG. 4A.Similarly, the symbols

$T_{21} = {{\frac{( {S_{1} + S_{2}} )}{\sqrt{2}}\mspace{11mu} {and}\mspace{14mu} T_{22}} = \frac{( {{j\; S_{1}} - {j\; S_{2}}} )}{\sqrt{2}}}$

will be transmitted via antenna 1 and antenna 2, respectively, whenprecoding is done using precoding matrix P₂ as shown in FIG. 4B. Itshould be noted that precoding is done on an OFDM subcarrier levelbefore the IFFT operation as illustrated in FIGS. 4A and 4B.

In a pre-coded MIMO system, inverse operations are performed at thereceiver to recover the transmitted symbols. The received symbols aremultiplied with the inverse precoding matrices. The inverse precodingmatrices are given as:

$\begin{matrix}{{{{inv}( P_{1} )} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}},{{{inv}( P_{2} )} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}}} & (4)\end{matrix}$

It should be noted that the inverse of a unitary precoding matrix cansimply be obtained by taking the complex conjugate transpose of thepre-coding matrix. The transmitted symbols are decoded by multiplyingthe received symbol vector with the inverse pre-coding matrices.Therefore, the transmitted symbols are given as:

$\begin{matrix}{{{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}} \times {\frac{1}{\sqrt{2}}\begin{bmatrix}{S_{1} + S_{2}} \\{S_{1} - S_{2}}\end{bmatrix}}} = \begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}},{{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}} \times {\frac{1}{\sqrt{2}}\begin{bmatrix}{S_{1} + S_{2}} \\{{j\; S_{1}} - {j\; S_{2}}}\end{bmatrix}}} = {\begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}.}}} & (5)\end{matrix}$

A downlink physical channel corresponds to a set of resource elementscarrying information originating from higher layers. First, a pluralityof information bits are coded with a plurality of code words to generatea plurality of blocks. For the downlink transmission in a physicalchannel, the block of bits b^((q))(0), . . . , b^((q))(M_(bit) ^((q))−1)in each code word q, shall be scrambled prior to modulation, resultingin a block of scrambled bits c^((q))(0), . . . , c^((q))(M_(bit)^((q))−1). Here, M_(bit) ^((q)) is the number of bits in code word q tobe transmitted on the physical downlink channel. Up to two code wordscan be transmitted in one subframe, i.e., qε{0,1}. Then, the block ofscrambled bits c^((q))(0), . . . , c^((q))(M_(bit) ^((q))−1) for eachcode word q shall be modulated using either Quadrature phase-shiftkeying (QPSK), or order-16 Quadrature amplitude modulation (16QAM), ororder-64 Quadrature amplitude modulation (64QAM), resulting in a blockof complex-valued modulation symbols d^((q))(0), . . . ,d^((q))(M_(symb) ^((q))−1). The complex-valued modulation symbols foreach of the code words to be transmitted are mapped onto one or severaltransmission layers. Complex-valued modulation symbols d^((q))(0), . . ., d^((q))(M_(symb) ^((q))−1) for code word q shall be mapped onto thelayers x(i)=[x⁽⁰⁾(i) . . . x^((ν-1))(i)]^(T) according to a certaincodeword-to-layer mapping scheme described in Section 5.3.3 of 3GPP TS36.211, where ν is the number of layers. Subsequently, a block ofvectors x(i)=[x⁽⁰⁾(i) . . . x^((ν-1))(i)]^(T) from the layer mapping isprecoded to generate a block of vectors y(i)=[y⁽⁰⁾(i) . . .y^((P−1))(i)]^(T), where P is the number of antenna ports and is equalto or larger than the rank ρ of the transmission. The block ofcomplex-valued symbols y^((p))(0), . . . , y^((p))(M_(s) ^((p))−1) shallbe mapped to resource elements (k,l) on antenna port p not used forother purposes in increasing order of first the index k and then theindex l.

We described a precoding approach that applies to both transmitdiversity and MIMO spatial multiplexing. A composite precoder isconstructed based on a unitary precoder such as Fourier matrix precodermultiplied with another unitary precoder representing a transmitdiversity scheme such as cyclic delay diversity. It should be noted thatthe principles of the current invention also applies to the cases ofnon-unitary precoding or unitary precoders other than Fourier matrixprecoder.

A Fourier matrix is a N×N square matrix with entries given by:

P _(N) =e ^(j2πmn/N) m,n=0,1, . . . (N−1)  (6)

For example, a 2×2 Fourier matrix can be expressed as:

$\begin{matrix}{P_{2} = {\begin{bmatrix}1 & 1 \\1 & ^{j\pi}\end{bmatrix} = {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}.}}} & (7)\end{matrix}$

Similarly, a 4×4 Fourier matrix can be expressed as:

$\begin{matrix}{P_{4} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & ^{{j\pi}/2} & ^{j\pi} & ^{{j3\pi}/2} \\1 & ^{j\pi} & ^{j2\pi} & ^{j3\pi} \\1 & ^{{j3\pi}/2} & ^{j3\pi} & ^{{j9\pi}/2}\end{bmatrix} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & j & {- 1} & {- j} \\1 & {- 1} & 1 & {- 1} \\1 & {- j} & {- 1} & j\end{bmatrix}.}}} & (8)\end{matrix}$

Multiple Fourier matrices can be defined by introducing a shiftparameter (g/G) in the Fourier matrix. The entry of the multiple Fouriermatrices is given by:

$\begin{matrix}{\begin{matrix}{P_{mn} = ^{{j2\pi}\frac{m}{N}{({n + \frac{g}{G}})}}} & {m,{n = 0},1,}\end{matrix}\ldots \mspace{11mu} {( {N - 1} ).}} & (9)\end{matrix}$

A set of four 2×2 Fourier matrices can be defined by taking G=4, andg=0, 1, 2 and 3, and are written as:

$\begin{matrix}{{P_{2}^{0} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},{P_{2}^{1} = \begin{bmatrix}1 & 1 \\^{{j\pi}/4} & {- ^{{j\pi}/4}}\end{bmatrix}},{P_{2}^{2} = \begin{bmatrix}1 & 1 \\^{{j\pi}/2} & {- ^{{j\pi}/2}}\end{bmatrix}},{P_{2}^{3} = {\begin{bmatrix}1 & 1 \\^{{j3\pi}/4} & {- ^{{j3\pi}/4}}\end{bmatrix}.}}} & (10)\end{matrix}$

A cyclic delay diversity scheme can be implemented in the frequencydomain with a phase shift of e^(jφ) ^(i) ^(k) applied to subcarrier ktransmitted from the i-th transmission antenna. The angle φ_(i) is givenas:

$\begin{matrix}{{\phi_{i} = {\frac{2\pi}{N}D_{i}}},} & (11)\end{matrix}$

where D_(i) is the cyclic delay in samples applied from the i-thantenna. It should be noted that other functions can be used to derivethe frequency domain phase shift. The phase shift may be kept constantfor a group of subcarriers. As shown in FIG. 6A, phase shift φ₁ isconstant over subband (SB) 1, φ₂ is constant SB2, and so on. It is alsopossible to allow the phase shift to vary from one group of subcarriersto the next. As shown in FIG. 6B, the phase shift varies from 2π/N to 2πover a frequency range from subcarrier 1 to subcarrier 512.

The cyclic delay diversity can be seen as precoding with the followingprecoding matrix for the case of four transmission antennas:

$\begin{matrix}{D_{4} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & ^{{j\phi}_{1}k} & 0 & 0 \\0 & 0 & ^{{j\phi}_{2}k} & 0 \\0 & 0 & 0 & ^{{j\phi}_{3}k}\end{bmatrix}.}} & (12)\end{matrix}$

FIG. 7 schematically illustrates a transmitter provided with the CDDpreceding scheme using the above precoding matrix. It can be noted thatthe same symbol with antenna and frequency (subcarrier) dependent phaseshifts are transmitted from multiple antenna. No phase shift is appliedfor the symbol transmitted from the first antenna.

In 3GPP RAN1 contribution R1-073096, “Text Proposal for 36.211 regardingCDD Design”, published in June 2007, Orlando, USA, a joint proposal isdepicted that includes both small and large delay CDD.

For zero-delay and small-delay CDD, precoding for spatial multiplexingshall be performed according to the following equation:

y(i)=D(i)·W(i)·x(i),  (13)

where the precoding matrix W(i) is of size P×ν, P is the number ofantenna ports, ν is the number of layers, the matrix D(i) is a diagonalmatrix for support of small or zero cyclic delay diversity, and thematrix x(i) denotes the signal to be transmitted on the i-th subcarrier.Here, x(i)=[x⁽⁰⁾(i) . . . x^((ν-1))(i)]^(T), where x^((j))(i) denotesthe signal to be transmitted on the i-th subcarrier in the j-th layer.The matrix D(i) shall be selected from Table 1, where a user equipment(UE)-specific value of δ is semi-statically configured in the UE and theNode B (i.e., the base station) by higher layers. The quantity η inTable 1 is the smallest number from a set {128, 256, 512, 1024, 2048},such that η≧N_(BW) ^(DL), with N_(BW) ^(DL) being the number ofsubcarriers in a downlink bandwidth.

TABLE 1 Zero and small delay cyclic delay diversity (TS 36.211, version1.1.0) Number δ of antenna Transmission No Small ports P D(i) rank ρ CDDdelay 1 [1] 1 — — 2 $\quad\begin{bmatrix}1 & 0 \\0 & e^{{- j}\; 2{\pi \cdot i \cdot \delta}}\end{bmatrix}$ 12 0 2/η 4 $\quad\begin{bmatrix}1 & 0 & 0 & 0 \\0 & e^{{- j}\; 2{\pi \cdot i \cdot \delta}} & 0 & 0 \\0 & 0 & e^{{- j}\; 2{\pi \cdot i \cdot 2}\delta} & 0 \\0 & 0 & 0 & e^{{- j}\; 2{\pi \cdot i \cdot 3}\delta}\end{bmatrix}$ 1234 0 1/η1/η1/η1/η

Note that these values apply only when transmit diversity is notconfigured for transmission rank 1.

For spatial multiplexing, the values of W(i) shall be selected among theprecoder elements in the codebook configured in the Node B and the UE.Node B can further confine the precoder selection in the UE to a subsetof the elements in the codebook using codebook subset restriction.According to TS 36.211, version 1.1.0, the configured codebook shall beequal to Table 2. Note that the number of layers ν is equal to thetransmission rank ρ in case of spatial multiplexing.

TABLE 2 Codebook for spatial multiplexing (TS 36.211, version 1.1.0)Number of Transmission antenna ports rank P ρ Codebook 1 1 [1] — — — — —2 1 $\quad\begin{bmatrix}1 \\0\end{bmatrix}$ $\quad\begin{bmatrix}0 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}$ — — — 4 1 2 3 4

According to TS 36.211, version 8.2.0, For transmission on two antennaports, pε{0,1}, the precoding matrix W(i) for zero, small, andlarge-delay CDD shall be selected from Table 3 or a subset thereof.

TABLE 3 Codebook for transmission on antenna ports {0,1}. (TS 36.211,version 8.2.0) Codebook Number of layers υ index 1 2 0$\quad\begin{bmatrix}1 \\0\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ 1 $\quad\begin{bmatrix}0 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}$ 3 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ — 4 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ — 5 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ —

For transmission on four antenna ports, pε={0,1,2,3}, the precodingmatrix w for zero, small, and large-delay CDD shall be selected fromTable 4 or a subset thereof. The quantity W_(n) ^({s}) denotes thematrix defined by the columns given by the set {s} from the expressionW_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n) where I is the 4×4 identitymatrix and the vector u_(n) is given by Table 4.

TABLE 4 Codebook for transmission on antenna ports {0, 1, 2, 3} (TS36.211, version 8.2.0) Codebook Number of layers ν index μ_(n) 1 2 3 4 0u₀ = [1 −1 −1 −1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀^({124})/{square root over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁^({1}) W₁ ^({12})/{square root over (2)} W₁ ^({123})/{square root over(3)} W₁ ^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{squareroot over (2)} W₂ ^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ =[1 j 1 −j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃^({123})/{square root over (3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 −j)/{square root over (2)} −j (1 − j)/{square root over (2)}]^(T) W₄^({1}) W₄ ^({14})/{square root over (2)} W₄ ^({124})/{square root over(3)} W₄ ^({1234})/2 5 u₅ = [1 (1 − j)/{square root over (2)} j (−1 −j)/{square root over (2)}]^(T) W₅ ^({1}) W₅ ^({14})/{square root over(2)} W₅ ^({124})/{square root over (3)} W₅ ^({1234})/2 6 u₆ = [1 (1 +j)/{square root over (2)} −j (−1 + j)/{square root over (2)}]^(T) W₆^({1}) W₆ ^({13})/{square root over (2)} W₆ ^({134})/{square root over(3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 + j)/{square root over (2)} j (1 +j)/{square root over (2)}]^(T) W₇ ^({1}) W₇ ^({13})/{square root over(2)} W₇ ^({134})/{square root over (3)} W₇ ^({1324})/2 8 u₈ = [1 −1 11]^(T) W₈ ^({1}) W₈ ^({12})/{square root over (2)} W₈ ^({124})/{squareroot over (3)} W₈ ^({1234})/2 9 u₉ = [1 −j −1 −j]^(T) W₉ ^({1}) W₉^({14})/{square root over (2)} W₉ ^({134})/{square root over (3)} W₉^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T) W₁₀ ^({1}) W₁₀ ^({13})/{square rootover (2)} W₁₀ ^({123})/{square root over (3)} W₁₀ ^({1324})/2 11 u₁₁ =[1 j −1 j]^(T) W₁₁ ^({1}) W₁₁ ^({13})/{square root over (2)} W₁₁^({134})/{square root over (3)} W₁₁ ^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T)W₁₂ ^({1}) W₁₂ ^({12})/{square root over (2)} W₁₂ ^({123})/{square rootover (3)} W₁₂ ^({1234})/2 13 u₁₃ = [1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃^({13})/{square root over (2)} W₁₃ ^({123})/{square root over (3)} W₁₃^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T) W₁₄ ^({1}) W₁₄ ^({13})/{square rootover (2)} W₁₄ ^({123})/{square root over (3)} W₁₄ ^({3214})/2 15 u₁₅ =[1 1 1 1]^(T) W₁₅ ^({1}) W₁₅ ^({12})/{square root over (2)} W₁₅^({123})/{square root over (3)} W₁₅ ^({1234})/2

For large-delay CDD, the precoding for spatial multiplexing shall beperformed according to the following equation:

y(i)=W(i)·D(i)·U·x(i),  (14)

where the precoding matrix W(i) is of size P×ν, P is the number ofantenna ports, ν is the number of layers, the quantity D(i) is adiagonal matrix for support of large cyclic delay diversity, and U is afixed matrix. The matrices U and D(i) are of size ν×ν. The elements ofthe fixed matrix U are defined as U_(mn)=e^(−j2πmn/ν), for m=0, 1, . . ., ν−1, and n=0, 1, . . . , ν−1. According to TS 36.211, version 1.1.0,the matrix D(i) shall be selected from Table 5.

TABLE 5 Large-delay cyclic delay diversity (TS 36.211, version 1.1.0)Number of antenna Transmission δ Large ports ^(P) rank ^(ρ) D(i) delay 11 — — 2 1 [1] 0 2 $\quad\begin{bmatrix}1 & 0 \\0 & e^{{- j}\; 2{\pi \cdot i \cdot \delta}}\end{bmatrix}$ 1/2 4 1 [1] 0 2 $\quad\begin{bmatrix}1 & 0 \\0 & e^{{- j}\; 2{\pi \cdot i \cdot \delta}}\end{bmatrix}$ 1/2 3 $\quad\begin{bmatrix}1 & 0 & 0 \\0 & e^{{- j}\; 2{\pi \cdot i \cdot \delta}} & 0 \\0 & 0 & e^{{- j}\; 2{\pi \cdot i \cdot 2}\delta}\end{bmatrix}$ 1/3 4 $\quad\begin{bmatrix}1 & 0 & 0 & 0 \\0 & e^{{- j}\; 2{\pi \cdot i \cdot \delta}} & 0 & 0 \\0 & 0 & e^{{- j}\; 2{\pi \cdot i \cdot 2}\delta} & 0 \\0 & 0 & 0 & e^{{- j}\; 2{\pi \cdot i \cdot 3}\delta}\end{bmatrix}$ 1/4

Note that the value of δ in Table 1 and the value of δ in Table 5 arenot the same.

According to TS 36.211, version 8.2.0, the matrices U and D(i) shall beselected from Table 6.

TABLE 6 Large-delay cyclic delay diversity (TS 36.211, version 8.2.0)Num- ber of layers ν U D(i) 1 [1] [1] 2$\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & e^{{- j}\; 2{\pi/2}}\end{bmatrix}$ $\quad\begin{bmatrix}1 & 0 \\0 & e^{{- j}\; 2{{\pi i}/2}}\end{bmatrix}$ 3 $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & 1 \\1 & e^{{- j}\; 2{\pi/3}} & e^{{- j}\; 4{\pi/3}} \\1 & e^{{- j}\; 4{\pi/3}} & e^{{- j}\; 8{\pi/3}}\end{bmatrix}$ $\quad\begin{bmatrix}1 & 0 & 0 \\0 & e^{{- j}\; 2{{\pi i}/3}} & 0 \\0 & 0 & e^{{- j}\; 4{{\pi i}/3}}\end{bmatrix}$ 4 $\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & e^{{- j}\; 2{\pi/4}} & e^{{- j}\; 4{\pi/4}} & e^{{- j}\; 6{\pi/4}} \\1 & e^{{- j}\; 4{\pi/4}} & e^{{- j}\; 8{\pi/4}} & e^{{- j}\; 12{\pi/4}} \\1 & e^{{- j}\; 6{\pi/4}} & e^{{- j}\; 12{\pi/4}} & e^{{- j}\; 18{\pi/4}}\end{bmatrix}$ $\quad\begin{bmatrix}1 & 0 & 0 & 0 \\0 & e^{{- j}\; 2{{\pi i}/4}} & 0 & 0 \\0 & 0 & e^{{- j}\; 4{{\pi i}/4}} & 0 \\0 & 0 & 0 & e^{{- j}\; 6{{\pi i}/4}}\end{bmatrix}$

For spatial multiplexing, the values of W(i) shall be selected among theprecoder elements in the codebook configured in the Node B and the UE.Node B can further confine the precoder selection in the UE to a subsetof the elements in the codebook using codebook subset restriction. Theconfigured codebook shall be equal to Table 3 and Table 4. Note that thenumber of layers ν is equal to the transmission rank ρ in case ofspatial multiplexing.

Furthermore, a codeword cycling method is proposed for the large delayequation, y(i)=D(i)·W(i)·U·x(i), so that W(i) is cyclically selected asone of the codeword in either the codebook in Table 3 for two antennaports, and in Table 4 for four antenna ports, or a subset of thecodebooks. It is proposed that the codeword changes either everysubcarrier, or every ν subcarriers, where ν is the transmission rank.

In a first embodiment according to the principles of the presentinvention, we propose to perform codeword cycling in the large delay CDDmethod y(i)=W(i)·D(i)·U·x(i) for every resource block (RB) or everyinteger number of RBs. For LTE system one RB consists of twelvesubcarriers. Therefore, the codeword W(i) is selected according toW(i)=C_(k), where k is given by

$\begin{matrix}{k = \{ \begin{matrix}{1,} & {{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{12m} \rceil,N} )}} = 1} \\{2,} & {{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{12m} \rceil,N} )}} = 2} \\\; & \vdots \\{N,} & {{{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{12m} \rceil,N} )}} = 0},}\end{matrix} } & (15)\end{matrix}$

or, more concisely,

$k = {{{mod}( {{\lceil \frac{i}{12m} \rceil - 1},N} )} + 1.}$

Here m>0 is a non-negative integer and 12 is the number of subcarriersin a RB. Furthermore, C_(k) denotes the k-th codeword in the single-userMIMO (SU-MIMO) precoding codebooks defined in Table 3 for two antennaports, and in Table 4 for four antenna ports, or a subset thereof, and Nis the codebook size or the size of the subset. Also note that mod(x) isa modulo operation and ┌x┐ is a ceiling operation.

In a second embodiment according to the principles of the presentinvention, we propose to perform codeword cycling in the small delay CDDmethod y(i)=D(i)·W(i)·x(i) for every q subcarriers. Therefore, thecodeword W(i) is selected according to W(i)=C_(k), where k is given by

$\begin{matrix}{k = \{ \begin{matrix}{1,} & {{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{q} \rceil,N} )}} = 1} \\{2,} & {{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{q} \rceil,N} )}} = 2} \\\; & \vdots \\{N,} & {{{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{q} \rceil,N} )}} = 0},}\end{matrix} } & (16)\end{matrix}$

or, more concisely,

$k = {{{mod}( {{\lceil \frac{i}{q} \rceil - 1},N} )} + 1.}$

Here q>0 is an arbitrary non-negative integer. Examples of q valueinclude q=1, or q=ν where ν is the transmission rank, or q=12 m (cycleevery m RBs) where m>0 is a non-negative number and 12 is the number ofsubcarriers in a RB. Furthermore, C_(k) denotes the k-th codeword in thesingle-user MIMO (SU-MIMO) precoding codebooks defined in Table 3 fortwo antenna ports, and in Table 4 for four antenna ports, or a subsetthereof, and N is the codebook size or the size of the subset. Also notethat mod(x) is a modulo operation and ┌x┐ is a ceiling operation.

In a third embodiment according to the principles of the presentinvention, we propose to perform codeword cycling in a uniform small andlarge delay CDD method as given by:

y(i)=D(i)·W(i)·C(i)·x(i)  (17)

for every q subcarriers. In the above equation, D(i) stands for adiagonal matrix for support of small delay CDD operation and D(i) shallbe selected from Table 1 for the i-th subcarrier, C(i) stands for of thelarge delay CDD operation for the i-th subcarrier, and C(i)=D′(i)·U,where D′(i) is a diagonal matrix for support of large delay CDDoperation, and U is a fixed matrix. The matrices D′(i) and U are of sizeν×ν, and shall be selected from Table 6. Therefore, the codeword W(i) isselected according to W(i)=C_(k), where k is given by:

$\begin{matrix}{k = \{ \begin{matrix}{1,} & {{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{q} \rceil,N} )}} = 1} \\{2,} & {{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{q} \rceil,N} )}} = 2} \\\; & \vdots \\{N,} & {{{{if}\mspace{14mu} {{mod}( {\lceil \frac{i}{q} \rceil,N} )}} = 0},}\end{matrix} } & (18)\end{matrix}$

or, more concisely,

$k = {{{mod}( {{\lceil \frac{i}{q} \rceil - 1},N} )} + 1.}$

Here q>0 is an arbitrary non-negative integer. Examples of q valueinclude q=1, or q=ν where ν is the transmission rank, or q=12 m (cycleevery m RBs) where m>0 is a non-negative number and 12 is the number ofsubcarriers in a RB. Furthermore, C_(k) denotes the k-th codeword in thesingle-user MIMO (SU-MIMO) precoding codebooks defined in Table 3 fortwo antenna ports, and in Table 4 for four antenna ports, or a subsetthereof, and N is the codebook size or the size of the subset. Also notethat mod(x) is a modulo operation and ┌x┐ is a ceiling operation.

In a fourth embodiment according to the principles of the presentinvention, we propose to apply different codewords for differentretransmission in a Hybrid automatic repeat-request (HARQ) system thatuses either the small-delay CDD method y(i)=D(i)·W(i)·x(i), or the largedelay method y(i)=W(i)·D(i)·U·x(i), or the uniform small-large delaymethod y(i)=D(i)·W(i)·C(i)·x(i). Let there be T re-transmissions in theHARQ system, and let W₁(i), W₂(i), . . . , W_(T)(i) be the codewordsused for these T retransmissions. The transmit signal for eachretransmission is then given by

y _(t)(i)=D(i)·W _(t)(i)·x(i)  (19)

for small delay CDD, and

y _(t)(i)=W _(t)(i)·D(i)·U·x(i)  (20)

for large delay CDD, and

y _(t)(i)=D(i)·W _(t)(i)·C(i)·x(i)  (21)

for uniform small and large delay CDD. Furthermore, we propose to selectthese codewords in such a way that W_(t)(i)=C_(k) _(t) , for t=1, . . ., T, where C_(k) _(t) denotes the k_(t)-th codeword in the codebook ofthe precoding codebook defined in Table 3 for two antenna ports, and inTable 4 for four antenna ports, or a subset thereof, and such that thechoice of C_(k) _(t) is independent for each retransmission, i.e, forthe t-th transmission, C_(k) _(t) can be any of the N codewords,regardless of which codeword is used in the previous transmissions. FIG.8 illustrates how the different codewords are used in differentre-transmissions.

In a fifth embodiment according to the principles of the presentinvention, we propose to add a pre-coding process, denoted by matrixW(i) where i is the subcarrier index, at the output of the rank-2 spacefrequency block code (SFBC) block given by:

$\begin{matrix}{{A = \begin{bmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}^{*} \\S_{3} & {- S_{4}^{*}} \\S_{4} & S_{3}^{*}\end{bmatrix}},} & (22)\end{matrix}$

and this precoded rank-2 method is illustrated in FIG. 9. And theoverall transmit signal is given by:

y(i)=W(i)·A(i),  (23)

where we used the notation A(i) to emphasize the fact that the rank-2SFBC transmission matrix is a function of the subcarrier index. That is,

$\begin{matrix}{{A(i)} = {\begin{bmatrix}{S_{1}(i)} & {- {S_{2}^{*}(i)}} \\{S_{2}(i)} & {S_{1}^{*}(i)} \\{S_{3}(i)} & {- {S_{4}^{*}(i)}} \\{S_{4}(i)} & {S_{3}^{*}(i)}\end{bmatrix}.}} & (24)\end{matrix}$

In addition, note that S₁ to S₄ are generated from the same codeword.

One way to choose the codeword is to choose the W(i) according to theprecoding matrix index (PMI) in the feedback, and W(i) belongs thecodebook defined in Table 3 for two antenna ports, and in Table 4 forfour antenna ports, or a subset thereof.

Another way to choose the codeword is to choose W(i) as an arbitraryunitary matrix that varies every q subcarriers, where q>0 is anarbitrary non-negative integer. Therefore, the codeword W(i) is selectedaccording to W(i)=C_(k), where k is given by:

$\begin{matrix}{k = \{ \begin{matrix}{1,} & {{{if}\mspace{14mu} {{mod}( {\lceil \frac{}{q} \rceil,N} )}} = 1} \\{2,} & {{{if}\mspace{14mu} {{mod}( {\lceil \frac{}{q} \rceil,N} )}} = 2} \\{N,} & {{{{if}\mspace{14mu} {{mod}( {\lceil \frac{}{q} \rceil,N} )}} = 0},}\end{matrix} } & (25)\end{matrix}$

or, more concisely,

$k = {{{mod}( {{\lceil \frac{}{q} \rceil - 1},N} )} + 1.}$

Examples of q value include q=1, or q=ν where ν is the transmissionrank, or q=12 m (cycle every mRBs) where m>0 is a non-negative numberand 12 is the number of subcarriers in a RB. Furthermore, C_(k) denotesthe k-th codeword in the single-user MIMO (SU-MIMO) precoding codebookdefined in Table 3 for two antenna ports, and in Table 4 for fourantenna ports, or a subset thereof, and N is the codebook size or thesize of the subset. Also note that mod(x) is a modulo operation and ┌x┘is a ceiling operation.

In a sixth embodiment according to the principles of the presentinvention, we propose to apply different codewords for differentretransmission in a Hybrid automatic repeat-request (HARQ) system thatuses the rank-2 SFBC transmission. Let there be T re-transmissions inthe HARQ system, and let W₁(i), W₂(i), . . . , W_(T)(i) be the codewordused for these T retransmissions, the transmit signal for eachretransmission is then given by:

y _(t)(i)=W _(t)(i)·A(i).  (26)

Furthermore, we propose to select these codewords in such a way thatW_(t)(i)=C_(k) _(t) for t=1, . . . , T, where C_(k) _(t) denotes thek_(t)-th codeword in the codebook of the precoding codebook defined inTable 3 for two antenna ports, and in Table 4 for four antenna ports, ora subset thereof, and such that the choice of C_(k) _(t) is independentfor each retransmission, i.e, for the t-th transmission, C_(k) _(t) canbe any of the N codewords, regardless of which codeword is used in theprevious transmissions. FIG. 10 illustrates how the different codewordsare used in different re-transmissions.

In a seventh embodiment according to the principles of the presentinvention, we propose a scheme where mapping of symbols to antennas ischanged on repeated symbols as shown in FIG. 11. In this example weassumed that four symbols S₁, S₂, S₃ and S₄ are transmitted with onerepetition over eight subcarriers, or two groups of subcarriers in twosubframes, with four subcarriers in each group. In the first foursubcarriers, symbols S₁ and S₂ are transmitted on antennas ports ANT0and ANT1, while symbols S₃ and S₄ are transmitted on antennas ports ANT2and ANT3. On repetition in the last four subcarriers, the symbols S₁ andS₂ are transmitted on antennas ports ANT2 and ANT3 while symbols S₃ andS₄ are transmitted on antennas ports ANT0 and ANT1. This proposedmapping results in greater diversity gain compared to the transmissionwhere mapping does not change on repetition. This diversity gains stemsfrom the fact that after one repetition all the four symbols aretransmitted from all the four transmit antennas.

In the proposed mapping scheme, the transmission matrix T₁ shown belowis used for initial transmission:

$\begin{matrix}\begin{matrix}{T_{1} = \begin{bmatrix}T_{11} & T_{12} & T_{13} & T_{14} \\T_{21} & T_{22} & T_{23} & T_{24} \\T_{31} & T_{32} & T_{33} & T_{34} \\T_{41} & T_{42} & T_{43} & T_{44}\end{bmatrix}} \\{{= \begin{bmatrix}S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0 \\0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*}\end{bmatrix}},}\end{matrix} & (27)\end{matrix}$

where T_(ij) represents symbol transmitted on the ith antenna and thejth subcarrier or jth time slot (i=1, 2, 3, 4, j=1, 2, 3, 4) for thecase of 4-Tx antennas. When the same symbols are repeated, a differentmapping matrix T₂ shown below is used for transmission:

$\begin{matrix}\begin{matrix}{T_{2} = \begin{bmatrix}T_{11} & T_{12} & T_{13} & T_{14} \\T_{21} & T_{22} & T_{23} & T_{24} \\T_{31} & T_{32} & T_{33} & T_{34} \\T_{41} & T_{42} & T_{43} & T_{44}\end{bmatrix}} \\{= {\begin{bmatrix}0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*} \\S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0\end{bmatrix}.}}\end{matrix} & (28)\end{matrix}$

Note that the principles of the present invention may be applied todecoding information received from a transmitter. In this case, sincethe selection of precoding matrices is a function of time (subframenumber) and frequency (subcarrier number), the receiver can simplyobserve the subframe number and subcarrier number, and use the samefunction to figure out the precoder matrix. The dependence of theprecoding matrix selection on frequency is explicit from Equations (13)and (14). The dependence of the precoding matrix selection on time isexplicit in the HARQ transmission scheme.

While the present invention has been shown and described in connectionwith the preferred embodiments, it will be apparent to those skilled inthe art that modifications and variations can be made without departingfrom the spirit and scope of the invention as defined by the appendedclaims.

1. A method for transmission in a communication system, the methodcomprising: encoding a plurality of information bits to generate aplurality of coded bits; scrambling the plurality coded bits to generatea plurality of scrambled bits; modulating the plurality of scrambledbits to generate a plurality of modulation symbols; mapping theplurality of modulation symbols onto the subcarriers in at least onetransmission layer of a transmission resource; precoding the modulationsymbols by using a matrix for cyclic delay diversity and a set ofcodewords from a certain codebook to generate a plurality of precodedsymbols, with the codeword used for precoding the modulation symbolscorresponding to an i-th subcarrier being established by:W(i)=C _(k), where C_(k) is the k-th codeword in the set of codewords,with the index k being established by:${k = {{{mod}( {{\lceil \frac{}{q} \rceil - 1},N} )} + 1}},$where q is a certain positive integer, and N is the size of the set ofcodewords; and transmitting the precoded symbols via a plurality oftransmission antennas.
 2. The method of claim 1, comprised of theprecoded symbols corresponding to the i-th subcarrier being establishedby:y(i)=W(i)·D(i)·U·x(i), with: x(i) being a block of modulation symbolscorresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; U beinga certain fixed matrix and the elements of U being established byU_(mn)=e^(−j2πmn/ν) for m=0, 1, . . . , ν−1, and n=0, 1, . . . , ν−1;and D(i) being a diagonal matrix for supporting large delay cyclic delaydiversity.
 3. The method of claim 1, comprised of the precoded symbolscorresponding to the i-th subcarrier being established by:y(i)=D(i)·W(i)·x(i), with: x(i) being a block of modulation symbolscorresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; andD(i) being a diagonal matrix for supporting small delay cyclic delaydiversity.
 4. The method of claim 1, comprised of the precoded symbolscorresponding to the i-th subcarrier being established by:y(i)=D(i)·W(i)·C(i)·x(i), with: x(i) being a block of modulation symbolscorresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; D(i)being a first diagonal matrix for supporting small delay cyclic delaydiversity; and C(i) being a matrix established by C(i)=D′(i)·U, U beinga certain matrix, the elements of the matrix U being defined asU_(mn)=e^(−j2πmn/ν), for m=0, 1, . . . , ν−1, and n=0, 1, . . . , ν−1,and D′(i) being a second diagonal matrix for supporting large delaycyclic delay diversity.
 5. The method of claim 1, comprised of q=1. 6.The method of claim 1, comprised of q=ρ, where ρ is the transmissionrank.
 7. The method of claim 1, comprised of q=12 m, with m being apositive integer.
 8. The method of claim 1, further comprising precodingthe modulation symbols by using a Fourier matrix, with the entries ofthe Fourier matrix being established by:P _(N) =e ^(j2πmn/N), for m,n=0,1, . . . (N−1).
 9. The method of claim1, comprised of the set of code words comprising all of the codewords inthe certain codebook.
 10. The method of claim 1, comprised of the set ofcode words comprising a subset of codewords in the certain codebook. 11.A method for transmission in a communication system, the methodcomprising: encoding a plurality of information bits to generate aplurality of coded bits; scrambling the plurality coded bits to generatea plurality of scrambled bits; modulating the plurality of scrambledbits to generate a plurality of modulation symbols; mapping theplurality of modulation symbols onto the subcarriers in at least onetransmission layer of a transmission resource; and repeatedly precodingand transmitting the modulation symbols via a plurality of antennas byusing a matrix for cyclic delay diversity and applying differentcodewords for different retransmissions, with the codeword used forprecoding the modulation symbols corresponding to an i-th subcarrier fora t-th transmission being established by:W _(t)(i)=C _(k) _(t) , for t=1, . . . T, where T is the total number oftransmissions, C_(k) _(t) is the k_(t)-th codeword in a set of codewordsfrom a certain codebook, and k_(t) is independent of i.
 12. The methodof claim 11, comprised of the precoded symbols corresponding to the i-thsubcarrier for the t-th transmission being established by:y _(t)(i)=W _(t)(i)·D(i)·U·x(i), with: x(i) being a block of modulationsymbols corresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; U beinga certain fixed matrix and the elements of U being established byU_(mn)=e^(−j2πmn/ν) for m=0, 1, . . . , ν−1, and n=0, 1, . . . , ν−1;and D(i) being a diagonal matrix for supporting large delay cyclic delaydiversity.
 13. The method of claim 11, comprised of the precoded symbolscorresponding to the i-th subcarrier for the t-th transmission beingestablished by:y _(t)(i)=D(i)·W _(t)(i)·x(i), with: x(i) being a block of modulationsymbols corresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; andD(i) being a diagonal matrix for supporting small delay cyclic delaydiversity.
 14. The method of claim 11, comprised of the precoded symbolscorresponding to the i-th subcarrier for the t-th transmission beingestablished by:y _(t)(i)=D(i)·W _(t)(i)·C(i)·x(i), with: x(i) being a block ofmodulation symbols corresponding to the i-th subcarrier andx(i)=[x⁽⁰⁾(i) . . . x^((ν-1))(i)]^(T), where ν is the number oftransmission layers; D(i) being a first diagonal matrix for supportingsmall delay cyclic delay diversity; and C(i) being a matrix establishedby C(i)=D′(i) U, U being a certain matrix, the elements of the matrix Uare defined as U_(mn)=e^(−j2πmn/ν), for m=0, 1, . . . , ν1, and n=0, 1,. . . , ν−1, and D′(i) being a second diagonal matrix for supportinglarge delay cyclic delay diversity.
 15. The method of claim 11, furthercomprising precoding the modulation symbols by using a Fourier matrix,with the entries of the Fourier matrix being established by:P _(N) =e ^(j2πmn/N), for m,n=0,1, . . . (N−1).
 16. The method of claim11, comprised of the set of code words comprising all of the codewordsin the certain codebook.
 17. The method of claim 11, comprised of theset of code words comprising a subset of codewords in the certaincodebook.
 18. A method for transmission in a communication system, themethod comprising: encoding four symbols to be transmitted by using arank-2 space frequency block code to generate a rank-2 space frequencyblock of symbols, with the rank-2 space frequency block beingestablished by: ${A = \begin{bmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}^{*} \\S_{3} & {- S_{4}^{*}} \\S_{4} & S_{3}^{*}\end{bmatrix}},$ where S₁, S₂, S₃, S₄ are the four symbols to betransmitted; precoding the block of symbols by using a matrix for cyclicdelay diversity and a set of codewords from a certain codebook togenerate a plurality of precoded symbols, with the precoded symbol foran i-th subcarrier being established by:y(i)=W(i)·A(i) where W(i) is a precoding matrix selected from the set ofcodewords for the i-th subcarrier, and A(i) is the rank-2 spacefrequency block corresponding to the i-th subcarrier; and transmittingthe precoded symbols via a plurality of antennas.
 19. The method ofclaim 18, comprised of the precoding matrix W(i) being selected from theset of code words in dependence upon a precoding matrix index that isreceived in the i-th subcarrier.
 20. The method of claim 18, comprisedof the codeword W(i) being established by:W(i)=C _(k), where C_(k) is the k-th codeword in the set of codewords,with the index k being established by:${k = {{{mod}( {{\lceil \frac{}{q} \rceil - 1},N} )} + 1}},$where q is a certain positive integer, and N is the size of the set ofcodewords.
 21. The method of claim 20, comprised of q=1.
 22. The methodof claim 20, comprised of q=ρ, where ρ is the transmission rank.
 23. Themethod of claim 20, comprised of q=12 m, with m being a positiveinteger.
 24. The method of claim 18, comprised of the set of code wordscomprising all of the codewords in the certain codebook.
 25. The methodof claim 18, comprised of the set of code words comprising a subset ofcodewords in the certain codebook.
 26. A method for transmission in acommunication system, the method comprising: encoding four symbols to betransmitted by using a rank-2 space frequency block code to generate arank-2 space frequency block of symbols, with the rank-2 space frequencyblock being established by: ${A = \begin{bmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}^{*} \\S_{3} & {- S_{4}^{*}} \\S_{4} & S_{3}^{*}\end{bmatrix}},$ where S₁, S₂, S₃, S₄ are the four symbols to betransmitted; and repeatedly precoding and transmitting the block ofsymbols via a plurality of antennas by using a matrix for cyclic delaydiversity and applying different codewords for differentretransmissions, with the precoded symbols corresponding to the i-thsubcarrier for the t-th transmission being established by:y _(t)(i)=W _(t)(i)·A ^(T)(i), where W_(t)(i) is a precoding matrixselected from a set of codewords from among a certain codebook for thei-th subcarrier and the t-th transmission.
 27. The method of claim 26,comprised of the precoding matrix W_(t)(i) being established by:W _(t)(i)=C _(k) _(t) , for t=1, . . . , T, where T is the total numberof transmissions, C_(k) _(t) is the k_(t)-th codeword in the set ofcodewords, and k_(t) is independent of i.
 28. The method of claim 26,comprised of the set of code words comprising all of the codewords inthe certain codebook.
 29. The method of claim 26, comprised of the setof code words comprising a subset of codewords in the certain codebook.30. A method for transmission in a communication system, the methodcomprising: encoding four symbols to be transmitted to generate twotransmission matrices, with the two transmission matrices T₁ and T₂being respectively established by: $\begin{matrix}{T_{1} = \begin{bmatrix}T_{11} & T_{12} & T_{13} & T_{14} \\T_{21} & T_{22} & T_{23} & T_{24} \\T_{31} & T_{32} & T_{33} & T_{34} \\T_{41} & T_{42} & T_{43} & T_{44}\end{bmatrix}} \\{{= \begin{bmatrix}S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0 \\0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*}\end{bmatrix}},}\end{matrix}$ and $\begin{matrix}{T_{2} = \begin{bmatrix}T_{11} & T_{12} & T_{13} & T_{14} \\T_{21} & T_{22} & T_{23} & T_{24} \\T_{31} & T_{32} & T_{33} & T_{34} \\T_{41} & T_{42} & T_{43} & T_{44}\end{bmatrix}} \\{= {\begin{bmatrix}0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*} \\S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0\end{bmatrix}.}}\end{matrix}$ where T_(ij) represents the symbol to be transmitted onthe ith antenna and one of the jth subcarrier and the jth subframe; andrepeatedly transmitting the four symbols via four antennas byalternatively applying the two transmission matrices T₁ and T₂ in one ofa frequency domain and a time domain.
 31. A wireless terminal in acommunication system, comprising: an encoding unit encoding a pluralityof information bits to generate a plurality of coded bits; a scramblingunit scrambling the plurality coded bits to generate a plurality ofscrambled bits; a modulating unit modulating the plurality of scrambledbits to generate a plurality of modulation symbols; a mapping unitmapping the plurality of modulation symbols onto the subcarriers in atleast one transmission layer of a transmission resource; a precodingunit precoding the modulation symbols by using a matrix for cyclic delaydiversity and a set of codewords from a certain codebook to generate aplurality of precoded symbols, with the codeword used for precoding themodulation symbols corresponding to an i-th subcarrier being establishedby:W(i)=C _(k), where C_(k) is the k-th codeword in the set of codewords,with the index k being established by:${k = {{{mod}( {{\lceil \frac{}{q} \rceil - 1},N} )} + 1}},$where q is a certain positive integer, and N is the size of the set ofcodewords; and a plurality of antennas transmitting the precodedsymbols.
 32. The wireless terminal of claim 31, comprised of theprecoded symbols corresponding to the i-th subcarrier being establishedby:y(i)=W(i)·D(i)·U·x(i), with: x(i) being a block of modulation symbolscorresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .(i)^((ν-1))(i)]^(T), where ν is the number of transmission layers; Ubeing a certain fixed matrix and the elements of U being established byU_(mn)=e^(−j2πmn/ν) for m=0, 1, . . . , ν−1, and n=0, 1, . . . , ν−1;and D(i) being a diagonal matrix for supporting large delay cyclic delaydiversity.
 33. The wireless terminal of claim 31, comprised of theprecoded symbols corresponding to the i-th subcarrier being establishedby:y(i)=D(i)·W(i)·x(i), with: x(i) being a block of modulation symbolscorresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; andD(i) being a diagonal matrix for supporting small delay cyclic delaydiversity.
 34. The wireless terminal of claim 31, comprised of theprecoded symbols corresponding to the i-th subcarrier being establishedby:y(i)=D(i)·W(i)·C(i)·x(i), with: x(i) being a block of modulation symbolscorresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; D(i)being a first diagonal matrix for supporting small delay cyclic delaydiversity; and C(i) being a matrix established by C(i)=D′(i)·U, U beinga certain matrix, the elements of the matrix U being defined asU_(mn)=e^(−j2πmn/ν), for m=0, 1, . . . , ν−1, and n=0, 1, . . . , ν−1,and D′(i) being a second diagonal matrix for supporting large delaycyclic delay diversity.
 35. The wireless terminal of claim 31, comprisedof q=1.
 36. The wireless terminal of claim 31, comprised of q=ρ, where ρis the transmission rank.
 37. The wireless terminal of claim 31,comprised of q=12 m, with m being a positive integer.
 38. The wirelessterminal of claim 31, further comprising a second precoding unitprecoding the modulation symbols by using a Fourier matrix, with theentries of the Fourier matrix being established by:P _(N) =e ^(j2πmn/N), for m,n=0,1, . . . (N−1).
 39. The wirelessterminal of claim 31, comprised of the set of code words comprising allof the codewords in the certain codebook.
 40. The wireless terminal ofclaim 31, comprised of the set of code words comprising a subset ofcodewords in the certain codebook.
 41. A wireless terminal in acommunication system, comprising: an encoding unit encoding a pluralityof information bits to generate a plurality of coded bits; a scramblingunit scrambling the plurality coded bits to generate a plurality ofscrambled bits; a modulation unit modulating the plurality of scrambledbits to generate a plurality of modulation symbols; a mapping unitmapping the plurality of modulation symbols onto the subcarriers in atleast one transmission layer of a transmission resource; and a precodingunit and a plurality of antennas repeatedly precoding and transmittingthe modulation symbols by using a matrix for cyclic delay diversity andapplying different codewords for different retransmissions, with thecodeword used for precoding the modulation symbols corresponding to ani-th subcarrier for a t-th transmission being established by:W _(t)(i)=C _(k) _(t) , for t=1, . . . , T, where T is the total numberof transmissions, C_(k) _(t) is the k_(t)-th codeword in a set ofcodewords from a certain codebook, and k_(t) is independent of i. 42.The wireless terminal of claim 41, comprised of the precoded symbolscorresponding to the i-th subcarrier for the t-th transmission beingestablished by:y _(t)(i)=W _(t)(i)·D(i)·U·x(i), with: x(i) being a block of modulationsymbols corresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; U beinga certain fixed matrix and the elements of U being established byU_(mn)=e^(−j2πmn/ν) for m=0, 1, . . . , ν−1, and n=0, 1, . . . , ν−1;and D(i) being a diagonal matrix for supporting large delay cyclic delaydiversity.
 43. The wireless terminal of claim 41, comprised of theprecoded symbols corresponding to the i-th subcarrier for the t-thtransmission being established by:y _(t)(i)=D(i)·W _(t)(i)·x(i), with: x(i) being a block of modulationsymbols corresponding to the i-th subcarrier and x(i)=[x⁽⁰⁾(i) . . .x^((ν-1))(i)]^(T), where ν is the number of transmission layers; andD(i) being a diagonal matrix for supporting small delay cyclic delaydiversity.
 44. The wireless terminal of claim 41, comprised of theprecoded symbols corresponding to the i-th subcarrier for the t-thtransmission being established by:y _(t)(i)=D(i)·W _(t)(i)·C(i)·x(i), with: x(i) being a block ofmodulation symbols corresponding to the i-th subcarrier andx(i)=[x⁽⁰⁾(i) . . . x^((ν-1))(i)]^(T), where ν is the number oftransmission layers; D(i) being a first diagonal matrix for supportingsmall delay cyclic delay diversity; and C(i) being a matrix establishedby C(i)=D′(i)·U, U being a certain matrix, the elements of the matrix Ubeing defined as U_(mn)=e^(−j2πmn/ν), for m=0, 1, . . . , ν−1, and n=,0,1, . . . , ν−1, and D′(i) being a second diagonal matrix for supportinglarge delay cyclic delay diversity.
 45. The wireless terminal of claim41, further comprising a second precoding unit precoding the modulationsymbols by using a Fourier matrix, with the entries of the Fouriermatrix being established by:P _(N) =e ^(j2πmn/N), for m,n=0,1, . . . (N−1).
 46. The wirelessterminal of claim 41, comprised of the set of code words comprising allof the codewords in the certain codebook.
 47. The wireless terminal ofclaim 41, comprised of the set of code words comprising a subset ofcodewords in the certain codebook.
 48. A wireless terminal in acommunication system, comprising: an encoding unit encoding four symbolsto be transmitted by using a rank-2 space frequency block code togenerate a rank-2 space frequency block of symbols, with the rank-2space frequency block being established by: ${A = \begin{bmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}^{*} \\S_{3} & {- S_{4}^{*}} \\S_{4} & S_{3}^{*}\end{bmatrix}},$ where S₁, S₂, S₃, S₄ are the four symbols to betransmitted; a precoding unit precoding the block of symbols by using amatrix for cyclic delay diversity and a set of codewords from a certaincodebook to generate a plurality of precoded symbols, with the precodedsymbol for an i-th subcarrier being established by:y(i)=W(i)·A(i) where W(i) is a precoding matrix selected from the set ofcode words for the i-th subcarrier, and A(i) is the rank-2 spacefrequency block corresponding to the i-th subcarrier; and a plurality ofantennas transmitting the precoded symbols.
 49. The wireless terminal ofclaim 48, comprised of the precoding matrix W(i) being selected from theset of code words in dependence upon a precoding matrix index that isreceived in the i-th subcarrier.
 50. The wireless terminal of claim 48,comprised of the codeword W(i) being established by:W(i)=C _(k), where C_(k) is the k-th codeword in the set of codewords,with the index k being established by:${k = {{{mod}( {{\lceil \frac{}{q} \rceil - 1},N} )} + 1}},$where q is a certain positive integer, and N is the size of the set ofcodewords.
 51. The wireless terminal of claim 50, comprised of q=1. 52.The wireless terminal of claim 50, comprised of q=ρ, where ρ is thetransmission rank.
 53. The wireless terminal of claim 50, comprised ofq=12 m, with m being a positive integer.
 54. The wireless terminal ofclaim 48, comprised of the set of code words comprising all of thecodewords in the certain codebook.
 55. The wireless terminal of claim48, comprised of the set of code words comprising a subset of codewordsin the certain codebook.
 56. A wireless terminal in a communicationsystem, comprising: an encoding unit encoding four symbols to betransmitted by using a rank-2 space frequency block code to generate arank-2 space frequency block of symbols, with the rank-2 space frequencyblock being established by: ${A = \begin{bmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}^{*} \\S_{3} & {- S_{4}^{*}} \\S_{4} & S_{3}^{*}\end{bmatrix}},$ where S₁, S₂, S₃, S₄ are the four symbols to betransmitted; and a precoding unit and a plurality of antennas repeatedlyprecoding and transmitting the block of symbols by using a matrix forcyclic delay diversity and applying different codewords for differentretransmissions, with the precoded symbols corresponding to the i-thsubcarrier for the t-th transmission being established by:y _(t)(i)=W _(t)(i)·A(i) where W_(t)(i) is a precoding matrix selectedfrom a set of codewords from among a certain codebook for the i-thsubcarrier and the t-th transmission.
 57. The wireless terminal of claim56, comprised of the precoding matrix W_(t)(i) being established by:W _(t)(i)=C _(k) _(t) , for t=1, . . . , T, where T is the total numberof transmissions, C_(k) _(t) is the k_(t)-th codeword in the set ofcodewords, and k_(t) is independent of i.
 58. The wireless terminal ofclaim 56, comprised of the set of code words comprising all of thecodewords in the certain codebook.
 59. The wireless terminal of claim56, comprised of the set of code words comprising a subset of codewordsin the certain codebook.
 60. A wireless terminal in a communicationsystem, comprising: an encoding unit encoding four symbols to betransmitted to generate two transmission matrices, with the twotransmission matrices T₁ and T₂ being respectively established by:$\begin{matrix}{T_{1} = \begin{bmatrix}T_{11} & T_{12} & T_{13} & T_{14} \\T_{21} & T_{22} & T_{23} & T_{24} \\T_{31} & T_{32} & T_{33} & T_{34} \\T_{41} & T_{42} & T_{43} & T_{44}\end{bmatrix}} \\{{= \begin{bmatrix}S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0 \\0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*}\end{bmatrix}},}\end{matrix}$ and $\begin{matrix}{T_{2} = \begin{bmatrix}T_{11} & T_{12} & T_{13} & T_{14} \\T_{21} & T_{22} & T_{23} & T_{24} \\T_{31} & T_{32} & T_{33} & T_{34} \\T_{41} & T_{42} & T_{43} & T_{44}\end{bmatrix}} \\{= {\begin{bmatrix}0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{4}^{*}} & S_{3}^{*} \\S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0\end{bmatrix}.}}\end{matrix}$ where T_(ij) represents the symbol to be transmitted onthe ith antenna and the jth subcarrier; and four antennas repeatedlytransmitting the four symbols by alternatively applying the twotransmission matrices T₁ and T₂ in one of a frequency domain or a timedomain.
 61. A method for communication in a wireless system, the methodcomprising: receiving a data packet via at least one antenna; selectinga precoding matrix from among a set of codewords in a certain codebookto be used to decode the data packet in dependence upon an index of thesubcarrier and an index of the subframe in which the data packet isreceived and in dependence upon an index of the precoding matrix withinthe set of codewords in the certain codebook, with the index of theprecoding matrix being established by:${k = {{{mod}( {{\lceil \frac{}{q} \rceil - 1},N} )} + 1}},$where k denotes the index of the precoding matrix in the set ofcodewords in the codebook, i denotes the index of the subcarrier inwhich the data packet is received, q denotes a certain positive integer,and N denotes the size of the set of codewords; and decoding thereceived data packet by using the selected precoding matrix.